SAT Math : SAT Mathematics
Study concepts, example questions & explanations for SAT Math
All SAT Math Resources
Example Questions
Example Question #3 : How To Find Rate
An arrow is launched at 10 meters per second. If the arrow flies at a constant velocity for an hour, how far has the arrow gone?
36,000 meters
3600 meters
100 meters
600 meters
36,000 meters
There are 60 seconds in a minute and 60 minutes in an hour, therefore 3600 seconds in an hour. The arrow will travel 3600x10= 36,000 meters in an hour.
Example Question #2 : How To Find Rate
If Jack ran at an average rate of 7 miles per hour for a 21 mile course, and Sam ran half as fast for the same distance, how much longer did it take for Sam to run the course than Jack?
2 hours
2.5 hours
3 hours
4 hours
1 hour
3 hours
Using the rate formula: Distance = Rate x Time,
Since Jack’s speed was 7 mph, Jack completed the course in 3 hours
21 = 7 x t
t = 3
Sam’s speed was half of Jack’s speed: 7/2 = 3.5
21 = 3.5 x t
t = 6
Therefore it took Sam 3 hours longer to run the course.
Example Question #4 : How To Find Rate
If a pail collects x ounces of dripping water every 15 minutes, how many ounces will it collect in h hours?
4x/h
15x/h
4xh
xh
15xh
4xh
Algebraic solution: First, convert minutes to hours.
60/15 = 4, so there are 4 15-minute increments in each hour. Therefore, 4x ounces of water are collected each hour. Multiply by h to get 4xh as the solution
Plug-in method: Just choose numbers.
x = 2
h = 3
If 2 ounces drip in 15 minutes, how many ounces will drip in one hour?
2/15 = x/60
15x = 120
x = 8
If 8 ounces drip in one hour, how many ounces will drip in 3 hours? (remember we chose that h = 3)
3 x 8 = 24
This is the answer we are looking for.
Plug x = 2, and h = 3 into each answer choice, to determine which will work. Remember you must plug into every answer choice in case more than one works. In that case, choose different values for x and h, and plug into only the choices that worked the first time.
Example Question #24 : Proportion / Ratio / Rate
Mary can make 20 snowballs in an hour. Mark can make 15 snowballs in 30 minutes. If they work together, how long will it take them to make 150 snowballs?
2.5 hours
185 minutes
120 minutes
3 hours
3 hours
If Mark makes 15 snowballs in 30 minutes, he can make 30 snowballs in an hour. Working together they can 50 snowballs in one hour. 150 snowballs divided by the amount they can make in one hour (50) will give us the total time it will take them to make 150 snowballs. In this case, 3 hours.
Example Question #31 : Proportion / Ratio / Rate
Car X used 4 gallons of gas in one week, and gets 10 miles to the gallon. If car Y went the same number of miles but only gets 8 miles to the gallon, how much gas did car Y use?
5 gallons
8 gallons
10 gallons
4 gallons
5 gallons
We first use the data for car X to conclude that car X went 40 miles (4gallons*10mi/gallon). We then use 40 miles for car Y, and divide 40 by 8, to give us 5 gallons of gas.
Example Question #1581 : Psat Mathematics
Bob and Sally are doing chores. It takes them 10 hours to do one of their chores. Assuming everyone works at the same rate, how many of their friends would they need to get to help them to do their chores in 2 hours?
8
5
None of the above
10
8
Since the kids are trying to do their chores in one fifth of the time, they need five times as many people. Since they have two, five times as many would be ten. We subtract the two of them and that would mean they need 8 more people, giving us answer 8.
Example Question #51 : Fractions
A water tank holds 500 gallons of water. There is a hole in the tank that leaks out the water at rate of 100 mL/min. In how many days will the water tank contain only half of the water it holds originally? Note: 1 gallon = 3.785 L
6
6.5
7
8
7.5
6.5
1 gallon = 3.785L = 3785mL, half of the tank = 250*3785 = 946,250mL. To find the minutes, 946250mL/(100mL/min) = 9462.5min. Since 1 day=24hr*60min=1440min, the number of days =94625min/(1440min/day)=6.5 days
Example Question #11 : How To Find Rate
Alex runs around his school race track one time in 15 minutes and takes another 25 minutes to run around a second time. If the course is 4 miles long, what is his approximate average speed in miles per hour for the entire run?
10
8
4
6
6
15 + 25 = 40 minutes. 40 minutes is 2/3 of an hour. Distance = rate x time. Using this formula, we have 4 = (2/3) r. To solve for r we multiply both sides by (2/3). r = 6
Example Question #31 : Fractions
If a car travels 60 mph for 2 hours, 55 mph for 1.5 hours and 30 mph for 45 minutes, how far has the car traveled?
225 miles
145 miles
1552.5 miles
120 miles
202.5 miles
225 miles
Distance traveled = mph x hour
60mph x 2hours + 55mph x 1.5 hours + 30 mph x 45 minutes (or .75 hours) =
120 miles + 82.5 miles + 22.5 miles = 225 miles
Example Question #52 : Fractions
If an object travels at 1200 ft per hour, how many minutes does it take to travel 180 ft?
11 minutes
10 minutes
7 minutes
8 minutes
9 minutes
9 minutes
1200 ft per hour becomes 20 ft per second (divide 1200 by 60 because there are 60 minutes in an hour). 180/20 is 9, giving 9 minutes to travel 180 ft.
All SAT Math Resources
